X1013

INTERCEPT OF EULER LINE AND LINE X7X_108

< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3 }: Euler Line { 33, 63 }: Central Line L(33, 63) { 7, 108 }: Central Line L(7, 108) { 55, 92 }: Central Line L(55, 92) { 6, 162 }: Central Line L(6, 162) { 100, 281 }: Central Line L(100, 281) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_7 = GERGONNE POINT (0.5903, 0.2769) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_1013 = INTERCEPT OF EULER LINE AND LINE X(7)X(108) (0.5829, 0.3190) A B C X2 X3 X4 X33 X63 X7 X108 X55 X92 X6 X162 X100 X281 X1013 (a, b, c) = (5, 6, 7) | AB = 1

X1013 (INTERCEPT OF EULER LINE AND LINE X7X_108) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (\cos A + \cos B + \cos C) \cos A + (\sec A + \sec B + \sec C) \cos B \cos C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(5.529367385342\)
▸ Incident Central Lines6 lines

{2, 3}, {6, 162}, {7, 108}, {33, 63}, {55, 92}, {100, 281}

Notes

As a point on the Euler line, X1013 has Shinagawa coefficients \((\$aS_{A}\$F, \$aS_{B}S_{C}\$)\).